exhaust, will vary directly with the work done, or under every condition of loading, the weight of steam per indicated horsepower must remain the same.

The author is well aware that authorities may not agree in every particular respecting the essential qualities of a perfect engine, and it is to be understood that the use of the term in this place only applies to a standard with which to compare the results obtained on actual engine trials.

The perfect engine is generally understood to be one working in a Carnot or reversible cycle, in which case the amount of heat and also the steam required, is perfectly definite and readily computed. This quantity was used as the^standard in the first comparisons made, but no satisfactory results could be obtained; it was found, however, that the formula; for 6team consumption which applied to the Carnot cycle, if slightly modified would give a standard, which agreed very closely with the results of the tests examined, consequently this latter quantity has been adopted as the standard.

The method of computing the amount of steam required for the standard engine is explained in the following paragraph:—

Amount Of Steam Required By The Perfect Engine.

The amount of steam required by the perfect engine will vary with the range of temperature through which the engine works. Its efficiency being expressed in each case by the difference of absolute temperature of entering (Tt) and exhaust (T3) steam divided by that of the entering steam.

The efficiency

T . T

* = (i)

This fraction expresses the greatest possible proportion of the entering heat that can bo transformed into work in any heat engine.

To find the heat units required for the perfect engine, we have only to divide 2545, the equivalent of one horse-power for one hour in B. T. U., by the efficiency expressed as above.

That is, the heat units, required by one 1. n. p. per hour by the perfect engine equals

2545 (2)

To find the number of pounds of steam required, this number is to be divided hy the available heat in one pound of the steam. Were the engine to work in a true Carnot's cycle, this available heat would be measured by the latent heat of the entering steam, since by that theory the amount equivalent to loss of temperature in expansion is restored by compression. The engine assumed to be perfect in this discussion, is somewhat different from the ideal engine of the Carnot cycle, although the required steam can be as readily calculated.

To obtain the steam consumption of an engine working in the Carnot cycle, the value given in equation (2) must be divided by the value of the latent heat (r) to obtain the steam consumption for the ideal engine adopted as standard, the value as given in equation (2) must be divided by the latent heat increased by a quantity equivalent to the loss of sensible heat of the steam in passing through the engine. That is, if r represents the latent heat in a pound of the entering steam, X the total heat, and q0 the heat of the liquid in the exhaust steam,

We should have

Steam required by the ideal )

engine of Carnot's cycle > =

per i. H. p. per hour. ) Tx \A)

X - Tt

Steam required by the stan- ) Qkak
dard engine per i. H. P. per V = ! = j)

hour-' 'T^rr2{l~qo)

That is, the standard engine as defined here does not work in a reversible cycle, but does utilize all available heat within limits of the temperature of entering steam and exhaust, whether it approximates more nearly or not to the real engine, it at least is the only value that can be used in expressing the economy in the propositions which follow.

The following table gives the amount of steam required by the standard engine per i. H. P. per hour for various conditions of steam pressure and exhaust, computed by formulas (4). This quantity is in the following discussion called the water-rate for the standard engine.

TABLE I. POUNDS OF DRY STEAM AND B. T. U. FEE I. H. P. REQUIRED BY THE 8TANDARD ENGINE.

Amount Of Steam Required To Overcome Wastes.

It is well known that no adequate theory has been as yet produced which will give a definite expression for these wastes, consequently they must be stated in empirical formula;, the accuracy of which can only be tested by comparison with results obtained by careful trial. These wastes are considered by Thurston1 to vary with the square root of the number of expansions, and by Cotterill to vary with a logarithmic function of the number of expansions. For four expansions or less the two propositions do not differ greatly.

In this case I desire to produce a practical rule that can easily be applied, and instead of using the number of expansions, which are often difficult to obtain from the data at hand, I have expressed all the results in terms of the indicated horse-power, consequently, while the expression may not be scientific in form, it is one that can readily be applied and used by practical engineers.

Two formulas will be employed, designated respectively A and B, both comparatively simple in their application, but giving best results when two cases, one less and one greater than most economical loads are considered.

Formula A is to be considered an application of the proposi

1. Se« "Manual of the Steam Engine," Part I., page 517. N. Y.: John Wiley & Son.

tion stated by Thurston in a modified form, i. e., that the wastes vary as the square roots of the ratio of variation in loading, instead of as the number of expansions. Formula B is a logarithmic function which was assumed by myself after a series of trials.

The two are used simply for the purpose of comparing two theories for variation in the wastes of an engine. In the discussion that follows, all the steam used by the real engine in excess of that required by the standard is considered as icaste. All comparisons are made with the real engine working with its most economical load. The following formulae are used :— Let m = the indicated horse-power (i. u. p.) of the engine for

most excellent results. Let w = the steam actually used per i. ir. p. per hour, when

engine*is developing m horse-power. hetp = the steam required for the perfect, i.e., the standard engine per i. H. P. per hour under same conditions. Let b = least waste of the engine = w — p. Let n = the horse-power of the engine for which the steam consumption is required.

Let x = — for power less than m.

n

Let x = — for power greater than m.

We shall have the following values for the steam consumption (y) per i. H. p. per hour:

First Case—n less than in.

y=p+h VTM~. (A) or,

n

V =p + b\/ 1 + (log M)^ ■ (B)

Second Case.—n greater than m.

TABLE FOR FACILITATING THE L'SE OF FORMULAE A AND B.

y = b V X + p . (A)

y = b V\ + (logeir)x +P- (B)

In applying the formulae, x is equal to the r. H. P. for most economical results divided by the actual 1. H. P. until the quotient is equal to one; it is then taken as the reciprocal of the above ratio. The results obtained by application of the formulas indicate that the effect, so far as changing the economy, is less for an overloaded than an underloaded engine.

A comparison with actual tests is given in the following pages.

Application Of Formulae To Actual Cases And Comparison With Actual Tests.

First. Triple expansion Corliss engine, made by E. P. Allis & Co., tested by C. H. Peabody, test reported at Am. Society Mech. Engineers ,November, 1892. Absolute steam pressure, 140.5 lbs., condensing engine; thermal efficiency, 30.2; steam required per 1. H. P. per hour for standard engine, 7.7 lbs.; best actual consumption, 13.74 lbs., for 125.3 1. H. P.

We have as formulae for this engine under the conditions of the test